**3. Methodology of Experimental Study on Roughness**

To perform the comparison of measurement characteristics between the image confocal microscope and some portable stylus measurement instrumentations, three specimens are measured. The first one is a milled part with the same tool and with different feed per tooth (measurand 1 to 7); The second one is a Type C1 spacing standard with grooves having a sine wave profile (measurand 8); The third one is a Type C4 spacing standard with grooves having an accurate profile (measurand 9). Figure 2 shows the three specimens, as well as their measurement areas.

**Figure 2.** (**a**) Measurands 1 to 7; (**b**) Measurand 8; (**c**) Measurand 9.

The technical features of the three instruments used in the comparison are detailed below:


**Figure 3.** Experimental setup. (**a**) *SP-1*; (**b**) *SP-2*; (**c**) *CM-3*.

#### **4. Analysis of Experimental Results**

The main aspects, as defined in Section 1, are analyzed below and will serve as a comparison of the evaluated methods, tactile and optical.

First, the repeatability study of the measurements made with the three instruments used in the comparison is developed. Measurand 8 is measured 25 times. Table 3 establishes the values obtained in this study. The standard deviations are similar for the three instruments, although the confocal microscope (*CM-3*) has the higher vertical resolution.


**Table 3.** Results of the repeatability study.

#### *4.1. Tactile Method*


measurands after applying the algorithm used for the evaluation of roughness parameters. As it can be observed, there were discrepancies between the values of the equipment, higher for the amplitude parameters (peak and valley), presenting differences between 11% and 17% of the value analyzed and minimal when evaluating the amplitude parameter (average of ordinates), with differences in percentage between 0.2% and 4%. The difference in the spacing parameter was due to the different x sampling value of each piece of equipment. When comparing measurands, better amplitude parameter results (average of ordinates) were obtained when a standard was evaluated (measurand 8). When the piece was measured, differences up to 12% were obtained due to the impossibility of measuring the same profile with different equipment, and the presence of irregularities in the surface of the piece. The uncertainty of the parameters was similar when a standard or a piece was measured. The amplitude parameters (peak and valley) presented values of uncertainty of hundredths of a micrometer and were at least one or two orders of magnitude higher than the uncertainty of the amplitude parameters (average of ordinates). This was due to the process of obtaining these parameters.




**Figure 4.** (**a**) *Rp* histogram; (**b**) *Rq* histogram.


**Table 5.** Correlation coefficient matrix of the roughness parameters.

**Table 6.** Roughness values obtained with the different instruments and methods (measurand 8).


**Table 7.** Roughness values obtained with the different instruments and methods (measurand 2).


*4.2. Confocal Microscope*


could be caused by local slope effects, which meant that the reflected light was not picked up by the target, or that the light intensity selected for the measurement was not adequate (low). On the contrary, if the luminous intensity of the equipment was very high, the CCD sensor could became saturated, tampering the peak position, and obtaining incorrect z-coordinate values. These effects could produce sharp peaks and valleys which were not real, as Figure 5b shows. Also, due to the geometry of the roughness profile, the illumination beam could only solve slopes with a maximum angle of 90 degrees. Very fine adjustment of the light intensity used in the measurement, and even the creation of different levels of illumination according to the depth of the sample, were therefore necessary. [37]. Likewise, it was be necessary to correct the unmeasured points and outliers by using interpolation and filtering techniques, respectively.


Finally, the compatibility between the results of the roughness parameters obtained by the different measurement methods and instruments and the values provided by the calibration certificate of the type C1 spacing standard (measurand 2) were analyzed. The calibrated parameters of the standard give the next values: Parameter *Ra* = 1.003 μm with an expanded uncertainty (*k* = 2) of 3% of the value of the parameter; Parameter *RSm* = 101.3 μm with an expanded uncertainty (*k* = 2) of 3 μm. When comparing the previous values with the uncertainty of the obtained measurements, it could be affirmed that the results were coherent with the certified values (the measured values were contained

in the interval characterized by the certified value and its expanded uncertainty). Figure 7a,b shows this consideration. It was verified that the values of the analyzed roughness parameters, obtained with the confocal microscope, always exceeded the certified values.

**Figure 5.** Roughness evaluated profile in measurand 2 (**a**) *SP-1*; (**b**) *CM-3*.

**Figure 6.** Roughness evaluated profile with a confocal microscope (outliers eliminated): (**a**) morphological filter application; (**b**) raw profile obtained after filtration; (**c**) waviness profile; (**d**) roughness profile.

**Figure 7.** Comparison of results for: (**a**) *Ra*; (**b**) *RSm*.

It should be noted that the present work has used parts that could be measured by any of the two considered techniques, optical or tactile. Therefore, the size and location of the measured parts had not been taken into account. Both size and location were factors of great relevance, which in many situations determine the type of measurement to be performed. In this sense, contact measurement techniques were usually advantageous compared to optical techniques due to the wide variety of existing profilometers, their portability, and the possibility of working in less restrictive environmental conditions.

#### **5. Conclusions**

This work has developed a comparative study between two kinds of measurement techniques that can be used in surface metrology, namely, two portable stylus profilometers (tactile) and a confocal microscope (optical). Measurement results, needed requirements, and available performances of both techniques have been analyzed. Both the metrological characteristics (measurement precision and accuracy, complexity of algorithms for data processing, etc.) and the operational characteristics (measuring ranges, measurement speed, environmental and operational requirements, costs, etc.) were studied.

The algorithms and procedures for calculating the uncertainties associated with the roughness parameters have been developed by employing the Monte Carlo method. The correlations between parameters have been found.

Measurements of several measurands obtained with the portable stylus profilometer have been shown to be the most reliable method when compared with the certified values of the measured standard, in line with Leach conclusions [2]. The procedure required little preparation and measurement time, and the measurement algorithms were simple. As a disadvantage, the low vertical resolution, i.e., the z-value, of the two instruments employed when compared to optical methods, could be neglected. With respect to the low x sampling value of the portable stylus profilometer employed, if compared with the confocal microscope, it could also be neglected. This conclusion, for other types of stylus profilometers with better metrological characteristics *r* (higher lateral resolution) that were not analyzed in this paper, may not be true.

The use of a confocal microscope allows for improving the previous parameters (lower uncertainty) at the expense of greater measurement and preparation times, as well as a very high cost of equipment. Besides, it forced the development of more complex algorithms due to the presence of outliers and points not measured on the sample in order to obtain reliable results. From the experimental study, it had been observed that when the confocal microscope was employed, it was possible to reduce nearly 10 times the difference between parameters (compared with results obtained with a stylus

profilometer) when the profile was filtered employing a morphological profile filter and a robust Gaussian regression filter.

Further studies would be suitable in order to include more terms that contribute to the uncertainty of the roughness parameters (standard contribution and sensor interaction (light or tip) among others).

**Author Contributions:** Conceptualization, A.S.L. and J.C.G.; Methodology, P.M.; Software, J.C.G.; Validation, C.W. and T.F.P.; Formal Analysis, A.S.L.; Investigation, P.M.; Resources, A.S.L.; Data Curation, T.F.P. and C.W.; Writing-Original Draft Preparation, J.C.G.; Writing-Review & Editing, J.C.G., P.M., and A.S.L.; Visualization, T.F.P.; Supervision, J.C.G.; Project Administration, A.S.L.; Funding Acquisition, A.S.L.

**Funding:** This work has been carried out within the framework of the Project DPI2016-78476-P "*Desarrollo colaborativo de patrones de software y estudios de trazabilidad e intercomparación en la caracterización metrológica de superficies*", belonging to the 2016 Call for R & D Projects corresponding to the State Program to Promote Scientific and Technical Research Excellence, State Subprogram of Generation of Knowledge.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
